Maximum Quasi-likelihood Estimation in Fractional Levy Stochastic Volatility Model

Bishwal, Jaya P. N.

doi:10.4236/jmf.2011.13008

Cited by 15 publications

(13 citation statements)

References 23 publications

(16 reference statements)

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“…The Hurst parameter can again be used to describe hop correlations because they share the same autocorrelation structure . The autocovariance function for fractional Lévy motion is where E [ L (1) 2 ] is the expected value of squared draws from the underlying Lévy distribution, effectively the distribution’s variance . In general, most Lévy stable distributions have an undefined variance due to their heavy tails.…”

Section: Methodsmentioning

confidence: 99%

“…where E[L(1) 2 ] is the expected value of squared draws from the underlying Levy distribution, effectively the distribution's variance. 52 In general, most Levy stable distributions have an undefined variance due to their heavy tails. However, normalizing eq 7 by the variance of a finite number of draws from a Levy stable distribution results in the same autocorrelation structure as fractional Brownian motion.…”

Section: Subordinated Fractional Levy Motion (Sflm)mentioning

confidence: 99%

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Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling

Coscia

Shirts

2020

J. Chem. Theory Comput.

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Fitting mathematical models with a direct connection to experimental observables to the outputs of molecular simulations can be a powerful tool for extracting important physical information from them. In this study, we present two new approaches that use stochastic time series modeling to predict long-time-scale behavior and macroscopic properties from molecular simulation, which can be generalized to other molecular systems where complex diffusion occurs. In our previous work, we studied long molecular dynamics (MD) simulation trajectories of a cross-linked H II phase lyotropic liquid crystal (LLC) membrane, where we observed subdiffusive solute transport behavior characterized by intermittent hops separated by periods of entrapment. In this work, we use our models to parameterize the behavior of the same systems, so we can generate characteristic trajectory realizations that can be used to predict solute mean-squared displacements (MSDs), solute flux, and solute selectivity in macroscopic length pores. First, using anomalous diffusion theory, we show how solute dynamics can be modeled as a fractional diffusion process subordinate to a continuous time random walk. From the MD simulations, we parameterize the distribution of dwell times, hop lengths between dwells, and correlation between hops. We explore two variations of the anomalous diffusion modeling approach. The first variation applies a single set of parameters to the solute displacements and the second applies two sets of parameters based on the solute's radial distance from the closest pore center. Next, we present an approach that generalizes Markov state models, treating the configurational states of the system as a Markov process where each state has distinct transport properties. For each state and transition between states, we parameterize the distribution and temporal correlation structure of positional fluctuations as a means of characterization and to allow us to predict solute MSDs. We show that both stochastic models reasonably reproduce the MSDs calculated from MD simulations. However, qualitative differences between MD and Markov state-dependent model-generated trajectories may in some cases limit their usefulness. With these parameterized stochastic models, we demonstrate how one can estimate the flux of a solute across a macroscopic length pore and, based on these quantities, the membrane's selectivity toward each solute. This work therefore helps to connect microscopic, chemically dependent solute motions that do not follow simple diffusive behavior with long-time-scale behavior, in an approach generalizable to many types of molecular systems with complex dynamics.

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Section: Methodsmentioning

confidence: 99%

Section: Subordinated Fractional Levy Motion (Sflm)mentioning

confidence: 99%

Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling

Coscia

Shirts

2020

J. Chem. Theory Comput.

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“…where W H t and B H t are two independent sub-fractional Brownian motions and ρ is the correlation between the interest rate and the elasticity. In order to estimate γt and its parameters based on the interest rate data, one can use the stochastic filtering method as in Bishwal [28].…”

Section: Test Function Estimator Of Elasticity Of Volatility and Stochastic Elasticity Modelmentioning

confidence: 99%

A New Algorithm for Approximate Maximum Likelihood Estimation in Sub-fractional Chan-Karolyi-Longstaff-Sanders Model

Bishwal

2021

AJPAS

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The paper introduces several approximate maximum likelihood estimators of the parameters of the sub-fractional Chan-Karolyi-Longstaff-Sanders (CKLS) interest rate model and obtains their rates of convergence. A new algorithm inspired by Newton-Cotes formula is presented to improve the accuracy of estimation. The estimators are useful for simulation of interest rates. The proposed new algorithm could be useful for other stochastic computation. It also proposes a generalization of the CKLS interest rate model with sub-fractional Brownian motion drivers which preserves medium range memory.

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“…See e.g. [2,8,9,12,15,28], and reference therein. Finally, Volterra processes (1.1) also provide suitable models in signal processing, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Fractional Calculus And Pathwise Integration for Volterra Processes Driven by Lévy and Martingale Noise

Nunno

Mishura

Ralchenko

2016

FCAA

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Abstract. We introduce a pathwise integration for Volterra processes driven by Lévy noise or martingale noise. These processes are widely used in applications to turbulence, signal processes, biology, and in environmental finance. Indeed they constitute a very flexible class of models, which include fractional Brownian and Lévy motions and it is part of the so-called ambit fields. A pathwise integration with respect of such Volterra processes aims at producing a framework where modelling is easily understandable from an information perspective. The techniques used are based on fractional calculus and in this there is a bridging of the stochastic and deterministic techniques. The present paper aims at setting the basis for a framework in which further computational rules can be devised. Our results are general in the choice of driving noise. Additionally we propose some further details in the relevant context subordinated Wiener processes.

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Maximum Quasi-likelihood Estimation in Fractional Levy Stochastic Volatility Model

Cited by 15 publications

References 23 publications

Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling

Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling

A New Algorithm for Approximate Maximum Likelihood Estimation in Sub-fractional Chan-Karolyi-Longstaff-Sanders Model

Fractional Calculus And Pathwise Integration for Volterra Processes Driven by Lévy and Martingale Noise

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